Problem: Simplify the following expression: $ q = \dfrac{-3}{10} + \dfrac{-6r - 8}{r + 3} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{r + 3}{r + 3}$ $ \dfrac{-3}{10} \times \dfrac{r + 3}{r + 3} = \dfrac{-3r - 9}{10r + 30} $ Multiply the second expression by $\dfrac{10}{10}$ $ \dfrac{-6r - 8}{r + 3} \times \dfrac{10}{10} = \dfrac{-60r - 80}{10r + 30} $ Therefore $ q = \dfrac{-3r - 9}{10r + 30} + \dfrac{-60r - 80}{10r + 30} $ Now the expressions have the same denominator we can simply add the numerators: $q = \dfrac{-3r - 9 - 60r - 80}{10r + 30} $ $q = \dfrac{-63r - 89}{10r + 30}$